Grad System and Units of Measurement

Date: 08/11/98 at 14:13:53
From: Greg MacNeill
Subject: Grad units of measurement
Hi,
I am having trouble finding information on one mode of operation for a
simple scientific calculator. Typically three systems of measurement
are provided: deg, rad and grad, which I assume represent degree,
radian and grad. As I understand, the grad system is commonly used in
Scandinavia and other northern European countries, particularly in
mapping.
How does the grad system compare to the degree system? Is it true that
the grad coordinate system is entirely consistent with metric
measurement? Apparently grad units of arc are directly related to the
metric linear equivalent. This is not the case of course with degrees
except in nautical applications where 1 minute of arc equals 1
nautical mile on the surface of the earth.
To achieve uniformity, perhaps we should measure all distances in
nautical miles or adopt the grad system for angle measurement.
Please let me know what you can about the basics of grad measurement.
Thanks,
Greg

Date: 08/14/98 at 15:39:27
From: Doctor Schwa
Subject: Re: Grad units of measurement
Grads are defined to be 100 in a right angle, for people who are
obsessed with the decimal system. Grad units of arc are related to the
metric system only in that way: a multiple of 10 is used in their
definition.
The original definition of kilometer was that there are 10,000 of
them between the equator and the north pole, so that 1 grad = 100 km,
1 centigrad = 1 km, would indeed be convenient for mapping in much the
same way as 1 minute = 1 nautical mile is. But of course that's just an
approximation - among other things, the Earth isn't particularly close
to a perfect sphere.
I side with the Babylonians - the convenience of 90 degrees being
evenly divisible by all kinds of things (most notably 3, which makes
the 30-60-90 triangle so easy to talk about) is well worth it.
- Doctor Schwa, The Math Forum
Check out our web site! http://mathforum.org/dr.math/